Three identical blocks move either on a horizontal surface, up a plane, or down a plane, as shown below.They all start with the same speed and continue to move until brought to rest by friction.Rank the three situations according to the mechanical energy dissipated by friction, least to greatest.
A)The same for all cases
B)1, 2, 3
C)1, then 2 and 3 tie
D)3, 1, 2
E)2, 1, 3

Question

Three identical blocks move either on a horizontal surface, up a plane, or down a plane, as shown below.They all start with the same speed and continue to move until brought to rest by friction.Rank the three situations according to the mechanical energy dissipated by friction, least to greatest. 
A)The same for all cases 
B)1, 2, 3 
C)1, then 2 and 3 tie 
D)3, 1, 2 
E)2, 1, 3

Quizplus · Accepted Answer

The mechanical energy dissipated by friction is equal to the work done by friction, which is equal to the force of friction multiplied by the distance the block travels before coming to rest.

1. On a horizontal surface, the force of friction is parallel to the surface and opposite the direction of motion. Therefore, the block will travel the farthest before coming to rest, which means that the distance the block travels before coming to rest is greater than the distances traveled by the blocks on the other surfaces. Since the force of friction is the same for all three cases, the work done by friction on the block on the horizontal surface will be the greatest.

2. On an up plane, the force of friction is parallel to the surface and opposite the direction of motion, but the force of gravity also acts on the block, which reduces the net force acting on the block. Therefore, the block will travel a shorter distance before coming to rest than the block on the horizontal surface.

3. On a down plane, the force of friction is parallel to the surface and in the direction of motion, which means that it acts to slow the block down more quickly than on the other surfaces. Therefore, the block will travel the shortest distance before coming to rest, which means that the work done by friction will be less than for the other two cases.

Therefore, the mechanical energy dissipated by friction will be least for the block on the down plane, followed by the block on the up plane, and greatest for the block on the horizontal surface. Thus, the answer is E, 2, 1, 3.

Three Identical Blocks Move Either on a Horizontal Surface, Up